Introduction to Statistical Analysis Summary

Statistics Theory

Different types of statistics
 Univariate
 Bivariate
 Multivariate
 Descriptive
o Summarize a specific data set
o Broken down into measures of tendency and measures of variability
 Inferential
o Random sample to describe and make inferences about the population

Inference
 A conclusion reached on the basis of evidence and reasoning

Unit of analysis
 The what or who is being studied
 Unit you draw conclusions about
 Typically all units are the same type of thing in a single data set
 Individuals, families, countries,…

Variable
 Measured property of each of the units of analysis
 Age, GDP, household income ….

Level of measurement
 Nominal
o Group classifications
o No meaningful ranking possible
o Numerical coding arbitrary
 Ordinal
o Meaningful ranking / ordering
o Distance between categories is unknown / not equal
 Interval
o Meaningful ranking
o Distances are equal
o No true zero point
 Ratio
o All properties of interval (ranking & equal distances)
o Absolute & meaningful zero point

Note: Need to know the level of measurement first in order to know which statistical
techniques to use for the given variable(s)

Continuous vs discrete variables
 Continuous variable
o Measured along a continuum
 Discrete variable

, o Measured in whole units or categories

Measures of central tendency
 Mean
o Interval / ratio
o All values added up and divided by n (number of observations in the sample)
o Changing any score will change mean
o Adding or removing a score will change mean (unless that score is already
equal to the mean)
o Adding, subtracting, multiplying, diving each score by a given value causes the
mean to change accordingly
o Sum of differences from the mean is zero
o Sum of squared differences from the mean is minimal

 Sum of Squares
o Squared distance from the mean
o A larger SS means that scores deviate more from the mean

 Median
o Ordinal & interval / ratio
o To find the median
 Sort all cases based on their value on x
 The value of the “middle case” equals the median (equal amount of
cases below and above)
o n is an even number -> median is mean value of the two middle cases
o not that sensitive to outliers as the mean
 mode
o nominal, ordinal, interval / ratio)
o mode is the category with the largest amount of cases

Measures of variability
 range
o ordinal, interval / ratio
o distance between highest and lowest score
o always reported together with maximum and minimum score
o sensitive to outliers
 Interquartile range (IQR)
o Ordinal, interval / ratio
o Based on “quartiles” that split our data into four equal groups of cases
o IQR based on distance between Q1 and Q3

Measures of variability
 Variance
o Interval / ratio
o Based on the sum of Squares
o For the calculation of variance, it matters whether we have sample data or
population data